numerical 2

Question 1

Suppose the risk premium of the market portfolio is estimated as 10%. What is the risk premium of a portfolio invested 60% in Apple and 40% in Exxon, if they have betas of 1.2 and 0.9 respectively? Please use the CAPM model.

Answer 1

With 60% in Apple and 40% in Exxon, portfolio beta = (0.6 * 1.2) + (0.4 *0.9) = 1.08 CAPM: E(rP) = rf + βP * [E(rM) - rf] E(rP) - rf = Risk Premium of Portfolio = βP * [E(rM) - rf] = 1.08 * (10) = 10.8 %

Question 2

2. Stock XYZ has an expected return of 12% and a beta = 1.2. Stock ABC has expected return of 15% and beta = 1.5. The market’s expected return is 11% and the risk free rate is 5%.

Answer 2

Given: E(rM) = 11; rf = 5. CAPM for Stock XYZ: E(rXYZ) = rf + βXYZ * [E(rM) - rf] = 5 + 1.2 * (11 - 5) = 12.2 Alpha for Stock XYZ = 12 - 12.2 = -0.2% CAPM for Stock ABC: E(rABC) = rf + βABC * [E(rM) - rf] = 5 + 1.5 * (11 - 5) = 14 Alpha for Stock ABC = 15 - 14 = +1% You should long Stock ABC because it has a positive alpha. You should short Stock XYZ because it has a negative alpha.

Question 3

The risk free rate is 3% and the expected return on market portfolio is 9%. A firm considers a project that is expected to have a beta of 1.4.

Answer 3

CAPM: E(rP) = rf + βP * [E(rM) - rf] = 3 + 1.4 * (9 - 3) = 3 + 8.4 = 11.4 The project should be accepted because the IRR exceeds the cost of capital

Question 4

The risk free rate is 4% and the expected return on market portfolio is 10%. Stock ABC has an expected return of 16%. If CAPM is the right model and Stock ABC is correctly priced, what is the beta of Stock ABC?

Answer 4

CAPM: E(rP) = rf + βP * [E(rM) - rf] 16 = 4 + βP * (10 - 4) 12 = βP * 6 Solving: βP = 2 è The Beta of Stock ABC = 2.